Question: Suppose $p$ and $q$ are inversely proportional. If $p=25$ when $q=6$, find the value of $p$ when $q=15$.
Solution: If $p$ and $q$ are inversely proportional, then $p\cdot{q}=k$ (where $k$ is a constant). We know that $p=25$ when $q=6$, so $(25)(6)=k$ or $k=150$. Thus when $q=15$, $(p)(15)=150$ and $p=\boxed{10}$.